Or to put it another way, it increases the amount of braking pressure for the same amount of pedal pressure.
So yes it can increase braking performance if you have a vehicle that doesn't stop very well.
If you have a vehicle that stops well it might not be an improvement.

I don't want to cause an argument, but!
A booster does not change "brake performance", the brakes are unchanged, only the pedal force is reduced for the same braking rate.
If you do a number of stops from speed with/without a booster, the brakes will still fade after the same number of stops.
Boosted brakes may "feel" better than non boosted but they don't actually stop any better.

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Find a job you love and you will never have to go to work !

I agree with Morris. You can call it reduced pedal effort, or MORE hydraulic pressure. If you cannot lock the wheels without a servo (looking for example at you, 997 Cooper or 850 brakes here) you CAN lock them with one.
This means yes, it can stop better, but maybe for only the 1st stop.
But whatever, it makes it feel like a modern car, not a Fred Flintstone one. I drove my road Mini with S brakes and no servo for 20 years, but after fitting a servo, I'm hooked.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

So your mini had drum brakes all round?

I had a `76 Clubby with drum brakes all round, then I put a set of 998 Cooper 7" discs on it, then added a VH44J servo and metal king pads. It then stopped very well, as a road car. Not as well as S brakes though.

My current Mini has S brakes, I drove it for 18 years with no servo, then fitted a VH44J because I had a recond one on the shelf. It stops like a modern car now. No way I'll go back to no servo.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

There will always be a difference in opinions. Years ago I put a VH44 on a drum brake mini and found that it did not help me at all pulling up from speed. They also made them a bit touchy so i removed it. Drums work well if serviced and adjusted on a regular basis. When i replied with a no, i took it as if the drum brakes were not performing well and there is another underlying issue that a servo wouldn't fix.

What do you mean by S brakes?

Cooper S/Clubman GT 7.5" front discs.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.